The Theory of Economic Complexity

Economic complexity methods have become popular tools in economic development, economic geography, and innovation. Yet, despite their widespread adoption, we lack a mechanistic model that provides these methods with a solid mathematical foundation. Here, we analytically derive the economic complexity eigenvector associated with a mechanistic model where the output of an economy in an activity (e.g. of a country in a product) depends on the combined presence of the factors required by the activity. Using analytical and numerical derivations we show that the economic complexity index (or ECI) is a monotonic function of the probability that an economy is endowed with many factors, validating the idea that it is an agnostic estimate of the presence of multiple factors of production. We then generalize this result to other production functions and to a short-run equilibrium framework with prices, wages, and consumption, showing that the derived wage function is consistent with economies converging to an income that is compatible with their complexity. Finally, we use this model to explain differences in the networks of related activities, such as the product space and the research space, showing that the shape of these networks can be explained by different factor distributions. These findings solve long standing puzzles in the economic complexity literature and validate commonly used metrics of economic complexity as estimates of the combined presence of multiple factors.